TSTP Solution File: SET027^7 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET027^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:15:20 EDT 2023
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 120
% Syntax : Number of formulae : 134 ( 52 unt; 9 typ; 33 def)
% Number of atoms : 418 ( 37 equ; 5 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 893 ( 95 ~; 45 |; 8 &; 555 @)
% ( 34 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 76 usr; 76 con; 0-3 aty)
% Number of variables : 159 ( 68 ^; 85 !; 6 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_eigen__0,type,
eigen__0: $i ).
thf(ty_eigen__3,type,
eigen__3: mu ).
thf(ty_eigen__2,type,
eigen__2: mu ).
thf(ty_member,type,
member: mu > mu > $i > $o ).
thf(ty_subset,type,
subset: mu > mu > $i > $o ).
thf(ty_eigen__1,type,
eigen__1: mu ).
thf(ty_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(ty_eigen__6,type,
eigen__6: mu ).
thf(h0,assumption,
! [X1: mu > $o,X2: mu] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__6,definition,
( eigen__6
= ( eps__0
@ ^ [X1: mu] :
~ ( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__6])]) ).
thf(sP1,plain,
( sP1
<=> ( ( exists_in_world @ eigen__1 @ eigen__0 )
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( subset @ eigen__1 @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) ) )
=> ~ ( ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( subset @ eigen__1 @ X1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( subset @ eigen__1 @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( exists_in_world @ eigen__3 @ eigen__0 )
=> ~ ( ( sP2
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) ) )
=> ~ ( ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) )
=> sP2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( exists_in_world @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( sP2
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) ) )
=> ~ ( ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) )
=> sP2 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( exists_in_world @ eigen__6 @ eigen__0 )
=> ( ( member @ eigen__6 @ eigen__1 @ eigen__0 )
=> ( member @ eigen__6 @ eigen__3 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( subset @ eigen__1 @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) ) )
=> ~ ( ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__1 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( subset @ eigen__1 @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( exists_in_world @ eigen__6 @ eigen__0 )
=> ( ( member @ eigen__6 @ eigen__2 @ eigen__0 )
=> ( member @ eigen__6 @ eigen__3 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ~ ( ( ( subset @ X2 @ X3 @ X1 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ( member @ X4 @ X3 @ X1 ) ) ) )
=> ~ ( ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ( member @ X4 @ X2 @ X1 )
=> ( member @ X4 @ X3 @ X1 ) ) )
=> ( subset @ X2 @ X3 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( subset @ eigen__2 @ eigen__3 @ eigen__0 )
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__2 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( exists_in_world @ eigen__2 @ eigen__0 )
=> ~ ( ( ( subset @ eigen__1 @ eigen__2 @ eigen__0 )
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__2 @ eigen__0 ) ) ) )
=> ~ ( ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__2 @ eigen__0 ) ) )
=> ( subset @ eigen__1 @ eigen__2 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP10
=> ~ ( ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__2 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) )
=> ( subset @ eigen__2 @ eigen__3 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP12
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( exists_in_world @ eigen__6 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ~ ( ( ( subset @ X1 @ X2 @ eigen__0 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ eigen__0 )
=> ( ( member @ X3 @ X1 @ eigen__0 )
=> ( member @ X3 @ X2 @ eigen__0 ) ) ) )
=> ~ ( ! [X3: mu] :
( ( exists_in_world @ X3 @ eigen__0 )
=> ( ( member @ X3 @ X1 @ eigen__0 )
=> ( member @ X3 @ X2 @ eigen__0 ) ) )
=> ( subset @ X1 @ X2 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( ( member @ eigen__6 @ eigen__1 @ eigen__0 )
=> ( member @ eigen__6 @ eigen__2 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( member @ eigen__6 @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( sP4
=> ~ sP13 ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( subset @ eigen__1 @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( exists_in_world @ eigen__2 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__1 @ eigen__0 )
=> ( member @ X1 @ eigen__2 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( sP20
=> sP22 )
=> ~ ( sP22
=> sP20 ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ( sP15
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( member @ eigen__6 @ eigen__1 @ eigen__0 )
=> ( member @ eigen__6 @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( sP18
=> ( member @ eigen__6 @ eigen__3 @ eigen__0 ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(sP27,plain,
( sP27
<=> ( member @ eigen__6 @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP27])]) ).
thf(sP28,plain,
( sP28
<=> ( subset @ eigen__2 @ eigen__3 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP28])]) ).
thf(sP29,plain,
( sP29
<=> ( member @ eigen__6 @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP29])]) ).
thf(sP30,plain,
( sP30
<=> ( exists_in_world @ eigen__1 @ eigen__0 ) ),
introduced(definition,[new_symbols(definition,[sP30])]) ).
thf(sP31,plain,
( sP31
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ( member @ X1 @ eigen__2 @ eigen__0 )
=> ( member @ X1 @ eigen__3 @ eigen__0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP31])]) ).
thf(sP32,plain,
( sP32
<=> ( sP21
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( subset @ eigen__2 @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__2 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) ) )
=> ~ ( ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__2 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( subset @ eigen__2 @ X1 @ eigen__0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP32])]) ).
thf(sP33,plain,
( sP33
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ~ ( ( ( subset @ eigen__2 @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__2 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) ) )
=> ~ ( ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ( member @ X2 @ eigen__2 @ eigen__0 )
=> ( member @ X2 @ X1 @ eigen__0 ) ) )
=> ( subset @ eigen__2 @ X1 @ eigen__0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP33])]) ).
thf(sP34,plain,
( sP34
<=> ( sP20
=> sP22 ) ),
introduced(definition,[new_symbols(definition,[sP34])]) ).
thf(def_meq_prop,definition,
( meq_prop
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
= ( X2 @ X3 ) ) ) ) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ( X1 @ X3 )
| ( X2 @ X3 ) ) ) ) ).
thf(def_mbox,definition,
( mbox
= ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
! [X4: $i] :
( ( (~) @ ( X1 @ X3 @ X4 ) )
| ( X2 @ X4 ) ) ) ) ).
thf(def_mforall_prop,definition,
( mforall_prop
= ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).
thf(def_mtrue,definition,
( mtrue
= ( ^ [X1: $i] : $true ) ) ).
thf(def_mfalse,definition,
( mfalse
= ( mnot @ mtrue ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).
thf(def_mimplied,definition,
( mimplied
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).
thf(def_mequiv,definition,
( mequiv
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).
thf(def_mxor,definition,
( mxor
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).
thf(def_mdia,definition,
( mdia
= ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( exists_in_world @ X3 @ X2 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mexists_ind,definition,
( mexists_ind
= ( ^ [X1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mexists_prop,definition,
( mexists_prop
= ( ^ [X1: ( $i > $o ) > $i > $o] :
( mnot
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).
thf(def_mreflexive,definition,
( mreflexive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] : ( X1 @ X2 @ X2 ) ) ) ).
thf(def_msymmetric,definition,
( msymmetric
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ X2 @ X3 )
@ ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mserial,definition,
( mserial
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).
thf(def_mtransitive,definition,
( mtransitive
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X3 @ X4 ) )
@ ( X1 @ X2 @ X4 ) ) ) ) ).
thf(def_meuclidean,definition,
( meuclidean
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X1 @ X3 @ X4 ) ) ) ) ).
thf(def_mpartially_functional,definition,
( mpartially_functional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( X3 = X4 ) ) ) ) ).
thf(def_mfunctional,definition,
( mfunctional
= ( ^ [X1: $i > $i > $o] :
! [X2: $i] :
? [X3: $i] :
( ( X1 @ X2 @ X3 )
& ! [X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X4 )
@ ( X3 = X4 ) ) ) ) ) ).
thf(def_mweakly_dense,definition,
( mweakly_dense
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( X1 @ X2 @ X3 )
@ ? [X5: $i] :
( ( X1 @ X2 @ X5 )
& ( X1 @ X5 @ X3 ) ) ) ) ) ).
thf(def_mweakly_connected,definition,
( mweakly_connected
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ( ( X1 @ X3 @ X4 )
| ( X3 = X4 )
| ( X1 @ X4 @ X3 ) ) ) ) ) ).
thf(def_mweakly_directed,definition,
( mweakly_directed
= ( ^ [X1: $i > $i > $o] :
! [X2: $i,X3: $i,X4: $i] :
( ^ [X5: $o,X6: $o] :
( X5
=> X6 )
@ ( ( X1 @ X2 @ X3 )
& ( X1 @ X2 @ X4 ) )
@ ? [X5: $i] :
( ( X1 @ X3 @ X5 )
& ( X1 @ X4 @ X5 ) ) ) ) ) ).
thf(def_mvalid,definition,
( mvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_msatisfiable,definition,
( msatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( X1 @ X2 ) ) ) ).
thf(def_mcountersatisfiable,definition,
( mcountersatisfiable
= ( ^ [X1: $i > $o] :
? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_minvalid,definition,
( minvalid
= ( ^ [X1: $i > $o] :
! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
| ( X1 @ X3 ) ) ) ) ).
thf(def_mdia_s4,definition,
( mdia_s4
= ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).
thf(prove_transitivity_of_subset,conjecture,
! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ~ ( ( subset @ X2 @ X3 @ X1 )
=> ~ ( subset @ X3 @ X4 @ X1 ) )
=> ( subset @ X2 @ X4 @ X1 ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ ! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ~ ( ( subset @ X2 @ X3 @ X1 )
=> ~ ( subset @ X3 @ X4 @ X1 ) )
=> ( subset @ X2 @ X4 @ X1 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_transitivity_of_subset]) ).
thf(h2,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ eigen__0 )
=> ( ~ ( ( subset @ X1 @ X2 @ eigen__0 )
=> ~ ( subset @ X2 @ X3 @ eigen__0 ) )
=> ( subset @ X1 @ X3 @ eigen__0 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP30
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ~ ( ( subset @ eigen__1 @ X1 @ eigen__0 )
=> ~ ( subset @ X1 @ X2 @ eigen__0 ) )
=> ( subset @ eigen__1 @ X2 @ eigen__0 ) ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
sP30,
introduced(assumption,[]) ).
thf(h5,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ eigen__0 )
=> ( ~ ( ( subset @ eigen__1 @ X1 @ eigen__0 )
=> ~ ( subset @ X1 @ X2 @ eigen__0 ) )
=> ( subset @ eigen__1 @ X2 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h6,assumption,
~ ( sP21
=> ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ~ ( sP20
=> ~ ( subset @ eigen__2 @ X1 @ eigen__0 ) )
=> ( subset @ eigen__1 @ X1 @ eigen__0 ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
sP21,
introduced(assumption,[]) ).
thf(h8,assumption,
~ ! [X1: mu] :
( ( exists_in_world @ X1 @ eigen__0 )
=> ( ~ ( sP20
=> ~ ( subset @ eigen__2 @ X1 @ eigen__0 ) )
=> ( subset @ eigen__1 @ X1 @ eigen__0 ) ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( sP4
=> ( ~ ( sP20
=> ~ sP28 )
=> sP2 ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP4,
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ ( sP20
=> ~ sP28 )
=> sP2 ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ ( sP20
=> ~ sP28 ),
introduced(assumption,[]) ).
thf(h13,assumption,
~ sP2,
introduced(assumption,[]) ).
thf(h14,assumption,
sP20,
introduced(assumption,[]) ).
thf(h15,assumption,
sP28,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP17
| ~ sP29
| sP18 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP24
| ~ sP15
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP26
| ~ sP18
| sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP8
| ~ sP15
| sP26 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP22
| sP24 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP31
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP10
| ~ sP28
| sP31 ),
inference(prop_rule,[status(thm)],]) ).
thf(8,plain,
( sP13
| sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP19
| ~ sP4
| ~ sP13 ),
inference(prop_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP33
| sP19 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP34
| ~ sP20
| sP22 ),
inference(prop_rule,[status(thm)],]) ).
thf(12,plain,
( sP23
| sP34 ),
inference(prop_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP32
| ~ sP21
| sP33 ),
inference(prop_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP11
| ~ sP21
| ~ sP23 ),
inference(prop_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP16
| sP32 ),
inference(all_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP7
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( sP25
| ~ sP27 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( sP25
| sP29 ),
inference(prop_rule,[status(thm)],]) ).
thf(19,plain,
( sP6
| ~ sP25 ),
inference(prop_rule,[status(thm)],]) ).
thf(20,plain,
( sP6
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(21,plain,
( sP12
| ~ sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).
thf(22,plain,
( ~ sP14
| ~ sP12
| sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(23,plain,
( sP5
| sP14 ),
inference(prop_rule,[status(thm)],]) ).
thf(24,plain,
( ~ sP3
| ~ sP4
| ~ sP5 ),
inference(prop_rule,[status(thm)],]) ).
thf(25,plain,
( ~ sP7
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(26,plain,
( ~ sP1
| ~ sP30
| sP7 ),
inference(prop_rule,[status(thm)],]) ).
thf(27,plain,
( ~ sP16
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(28,plain,
( ~ sP9
| sP16 ),
inference(all_rule,[status(thm)],]) ).
thf(subset_defn,axiom,
sP9 ).
thf(29,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,h4,h7,h10,h14,h15,h13,subset_defn]) ).
thf(30,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h15])],[h12,29,h14,h15]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,30,h12,h13]) ).
thf(32,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h9,h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,31,h10,h11]) ).
thf(33,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h9]),tab_negall(eigenvar,eigen__3)],[h8,32,h9]) ).
thf(34,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,33,h7,h8]) ).
thf(35,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,34,h6]) ).
thf(36,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,35,h4,h5]) ).
thf(37,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,36,h3]) ).
thf(38,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,37,h2]) ).
thf(39,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[38,h0]) ).
thf(0,theorem,
! [X1: $i,X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X1 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X1 )
=> ( ~ ( ( subset @ X2 @ X3 @ X1 )
=> ~ ( subset @ X3 @ X4 @ X1 ) )
=> ( subset @ X2 @ X4 @ X1 ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[38,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET027^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 13:01:32 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % Mode: cade22grackle2xfee4
% 0.21/0.47 % Steps: 1331
% 0.21/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------